本文研究一类三点边值条件下非线性三阶奇摄动边值问题 $\"\"$ 解的存在性和渐近估计, 其中0 < η < 1，0 < ξη < 1. 通过构造一个恰当的广义上下解对和运用Nagumo 条件和边界层函数,我们得到上述问题解的存在性,并且给出了解的一致有效渐近估计.
This paper is devoted to study the existence and asymptotic estimates of solutions for a class of nonlinear third-order singularly perturbed boundary value problems with three-point boundary value conditions $\"\"$ where 0 < η < 1, 0 < ξη < 1. By constructing an appropriate generalized upper- and lower-solution pair and employing the Nagumo conditions and boundary layer functions, we obtain the existence of solutions to the above problem and give uniformly valid asymptotic estimates of the solutions.